EP0833470A2 - Method of frame synchronization - Google Patents

Abstract

The method involves determining the temporal position of a synchronisation sequence in a received data stream for frame synchronisation, by using the principle of maximum likelihood theory. This determination is carried out from the received data stream before the frequency and phase synchronisation. The maximum correlation between the differentially decoded received data stream, with the receiver side known conjugate complex differentially decoded synchronisation stream, may be taken into account. In addition, a term for removing interference may be taken into account. The frame temporal position determination may be carried out also before the clock synchronisation. Alternatively it may be carried out after clock synchronisation.

Description

The invention relates and is based on a method to determine the timing of a synchronization sequence in a received data stream (frame synchronization) according to the preamble of the main claim.

A frame synchronization method of this type is known (James L. Massey: "Optimal Frame Synchronization", IEEE Trans. On Comm., Vol.Com.20, Apr. 1972, pp. 115-119 and R. Mehlan, H. Meyr: "Optimal Frame Synchronization For Asynchronous Packet Transmission ", ICC 1993 in Geneva, Vol.2 / 3, pp. 826-830). These used only Frame synchronization methods have the disadvantage that before the actual frame synchronization, a clock, Carrier and phase synchronization can be performed got to. Carrier and phase synchronization without first performed frame synchronization and thus without Knowledge of the data sequence is only possible with so-called Non-data-aided (NDA) process possible. When transferring of higher-level MQAM signals for such NDA method the theoretically permissible frequency deviation between transmitter and receiver 12.5% of the symbol rate, at MPSK even only 1 / M, · 50%. For TDMA transmissions possibly only your own burst for clock, phase and Carrier synchronization can be used and there is using the known frame synchronization method the further problem is that the timing of the burst due to the frame synchronization not yet carried out is not known and only through additional aids must be determined.

It is an object of the invention to provide a process for everyone linear modulation method for determining the temporal Location of a symbol sequence in a received data stream to show that avoids these disadvantages.

This task is based on a process Preamble of the main claim by its characterizing Features resolved.

Advantageous further developments, particularly with regard to a simple calculation of the carrier frequency deviation result from the subclaims.

Due to the conditions chosen according to the invention for the Application of the Maximu likelihood theory known per se it becomes possible to synchronize the frame immediately from the received data sequence before the carrier and Perform phase synchronization either before or after clock synchronization. So that is for the subsequent process steps such as clock synchronization or carrier and phase synchronization the temporal Location of the synchronization sequence already known and this means that the MQAM process or TDMA process avoided above disadvantages. As a consequence, that the theoretically permissible frequency deviation for all linear modulation methods are 50% of the symbol rate may.

The invention is described below with the aid of schematic drawings explained in more detail using exemplary embodiments.

1 schematically shows the processing on the transmitter side in general for linear modulation methods. In this case, several m bits of the serial data stream to be transmitted are combined in a series / parallel converter 1 to form a complex complex symbol a _{v of} higher value. The compact signal space comprises M elements. In this way, complex symbol values with real part a _{I, v} and imaginary part a _{Q, v are} generated in mapper 2, which are then added to the high-frequency signal to be transmitted by the carrier frequencies of a carrier generator 3, which are 90 ° out of phase with each other. In the case of offset modulation methods, a delay of half a symbol period T _s / 2 must also be carried out in the quadrature branch before the modulation.

das Verhältnis von Abtastfrequenz zur Symbolrate an. Fig. 2 shows the associated quadrature receiver. The received high-frequency signal is again mixed down into the baseband in two mixers 4 and 5 with the superimposed frequencies of a carrier oscillator 6, which are phase-shifted by 90 ° relative to one another, and then the baseband signals are generated by means of a clock generator 7, whose clock frequency f A = 1 / T A an integer multiple of the symbol rate f s = 1 / T s is sampled. The sampling rate must be chosen so large that the sampling theorem is fulfilled. The oversampling factor is given accordingly

the ratio of sampling frequency to symbol rate.

In contrast to the feedback demodulation method, the oscillator 6 is not based on the Carrier frequency and carrier phase readjusted, but the oscillator 6 is in its frequency a maximum permissible deviation of 50 percent of the symbol rate exactly on the transmitter side Carrier frequency set. The clock generator 7 is not regulated in its phase, only that Clock frequency is set to the value of the corresponding modulation method. The Subsequent further processing takes place in the arrangement 8, its function and mode of operation is described below.

FIG. 3 shows the transmission model described with reference to FIGS. 1 and 2 in the equivalent baseband representation. The starting point is the digital complex Dirac sequence weighted with the symbols to be transmitted

This signal can be represented as the sum of two Dirac impulses weighted with the symbol values a _{I, v} , a _{Q, v} at the times t = v · T s in real and imaginary part. The symbols a v = a I, v + Yes Q, v can assume the values a _{I, v} , a _{Q, v} ∈ {± 1, ± 3, ± 5, ···} for the modulation method MQAM. Other linear modulation methods such as π / 4-QPSK with a _{I, v} , a _{Q, v} ∈ {± 1 e ^{jvπ / 4} , ± each ^{jvπ / 4} } or the offset MQAM method are possible, in which the imaginary part a _{Q, v} is delayed by half a symbol period. The symbol sequence is then given to the transmission filter with the impulse response h _s ( t ).

The transmission signal s ( t ) is obtained by

The frequency offset Δ f and phase offset Δ Φ, which is unknown between the transmitter and the receiver, is taken into account by multiplying it with the rotary pointer e ^{j (2 π Δ ft + ΔΦ)} .

The time offset ε T _s unknown to the receiver compared to the ideal sampling times is realized by the following system block. The values ε are in the range -0.5 ≤ ε <0.5

da der Erwartungswert zeitabhängig und periodisch mit T_s ist. Die mittlere Symbolenergie des Sendesignals berechnet sich mit

The delayed transmission signal is disturbed on the transmission path by additive white Gaussian noise (AWGN) n ( t ), and the reception signal r ( t ) is generated. The noise signal is according to n ( t ) = n I. ( t ) + jn Q ( t ) complex value. The real part n _I ( t ) and the imaginary part n _Q ( t ) have the two-sided power density spectrum (LDS) N _0/2 and are statistically independent of each other. The average power of the transmitted signal s ( t ) results

since the expected value is time-dependent and periodic with T _s . The average symbol energy of the transmission signal is also calculated

FIG. 4 shows the synchronization concept with the input sequence x _v from FIG. 3. This sequence is used for clock synchronization with subsequent compensation with the estimated time offset - ε ∧ T _s . The clock synchronization takes place without knowledge of the transmitted symbols (non-data-aided) and is not critical. After subsampling by the oversampling factor ov , only the sample values r _{v are available} at the symbol instants free of intersymbol interference. In the offset method, the delay must be canceled by half the symbol period before the subsampling. The frame synchronization derived below can be carried out either by the non-timing-compensated sequence x _v or by the sequence r _v that is only present at the symbol times . The frame synchronization by the non-timing-compensated sequence x _v may be necessary, for example, if a TDMA system is present and only the burst that is not yet known in terms of time may be used for timing estimation. With frame synchronization with x _v , the remaining deviation from the symbol time (maximum half a sampling period) is then estimated and reversed by the clock synchronization.
Because of the simpler nomenclature, the procedure for the sequence r _v is derived. The derived method is also valid for the non-timing-compensated sequence x _v . The main difference is that because of the still unknown symbol time, the sync sequence does not have to be searched for in the symbol grid, but in the scanning grid. With frame synchronization by the sequence x _v , the sequence is not exactly at the symbol time and an additional error occurs due to intersymbol interference. In this case, therefore, the oversampling factor should be at least ov = 4 be.

5 shows the embedding of the sync sequence sync _v in the transmitted symbol sequence a _v . The length of the sync sequence is S symbols. The sync sequence begins after µ symbol periods after the time zero. The task of frame synchronization is to determine this temporal position, which is not known in the receiver. The sync sequence is known in the receiver. 4, µ = 2 is shown as an example. Processing in the receiver begins at the time zero. R sample values of the sequence r _v are evaluated for frame synchronization. It is further assumed that the length R of the reception vector r is chosen to be large enough to contain a complete sync sequence.

A. Clock synchronization

The sequence x _v in FIG. 4 is used to estimate the clock phase from the unknown standardized time offset ε. The clock synchronization method is feedback-free and known (K. Schmidt: Digital clock recovery for bandwidth-efficient mobile radio systems, dissertation, Inst. For communications engineering, Darmstadt, Dec. 1993 and Oerder: Algorithms for digital clock synchronization for data transmission, Chair of Electrical Control, Aachen, 1989) . The estimated time shift ε ∧ T _s (the roof is generally used for estimates) is then reversed by an interpolation filter. Subsequently, an oversampling by the oversampling factor ov is made and the symbols r still appear in the sequence r _v . Basic considerations on compensation can be found in (K. Schmidt: "Digital Clock Recovery for Bandwidth-Efficient Mobile Radio Systems", Dissertation, Inst. For Communication Technology, Darmstadt, Dec. 1993 and Kammeyer: "News Transmission", Teubner-Verlag, Stuttgart, 1992).

B. Frame synchronization

welche durch Variation des Versuchsparameters µ = [0,R - S] maximiert werden soll. Hierbei beschreibt v_rest gemäß

den v-Bereich des Vektors r außerhalb der vermuteten Syncfolge mit der Randomsymbolen a_v . Grundsätzlich werden die Versuchsparameter mit einer Schlange und Schätzparameter mit einem Dach versehen. In den nachfolgeden Schritten wird die Vereinbarung getroffen, daß alle für das Verfahren irrelevanten Therme zu eins gesetzt werden, ohne eine neue Funktion zu definieren.The starting point is the maximum likelihood function according to GI. (1)

which by varying the test parameter µ = [0, R - S ] should be maximized. Here v _{rest describes} according to

the v region of the vector r outside the assumed sync sequence with the random symbols a _v . Basically, the test parameters are provided with a snake and estimation parameters with a roof. In the following steps, the agreement is reached that all thermal baths that are irrelevant to the process are set to one without defining a new function.

Beim zweiten Therm in GI.(1) ist die Random-Folge a_v nicht bekannt, weshalb auch der Erwartungswert bzgl. dieser Folge gebildet werden muß:

Durch Ausnutzung der statistischen Unabhängigkeit der Symbole a_v ergibt sich weiterhin

Im folgenden wird von einem Störabstand E_s /N ₀>>1 ausgegangen. Dann läßt sich beim tatsächlichen Frequenz- und Phasenversatz GI.(3) durch

annähern. Da die Random-Folge a_v nicht bekannt ist, wird der Schätzwert |a ∧_v | verwendet. Man beachte, daß nicht das Symbol, sondern nur dessen Betrag geschätzt werden muß. Folglich ist hierfür keine Frequenz- und Phasensynchronisation notwendig. Durch Einsetzen der GIn.(2,4) in GI.(1) und anschließender Logarithmierung erhält man die Log-Likelihood-Funktion

Um bei den beiden Thermen gleiche Summationsgrenzen zu bekommen, wird zur Vereinfachung auf der rechten Seite von GI.(5) zusätzlich mit der von den Schätzparametern unabhängige Konstante

erweitert und erhält damit die Log-Likelihood-Funktion nach GI.(6)

Veranschaulichung: Der erste Therm in GI.(6) beschreibt eine Korrelation zwischen der frequenz-und phasenkompensierten Empfangsfolge mit der konjugiert komplexen Sync-Sequenz und der zweite Therm kann als Maßnahme zur Störbefreiung betrachtet werden. Das läßt sich einfach verstehen, wenn man von einer fehlerfreien Schätzung von |a ∧_v | ausgeht. Dann kann die Näherung

in GI.(6) eingesetzt werden und erhält bei exakter Frequenz- und Phasenkompensation

First, the first therm in GI. (1) is simplified and given GI. ( 2 )

The random sequence a _{v is} not known for the second therm in Eq. (1), which is why the expected value for this sequence must also be formed:

By using the statistical independence of the symbols a _{v, the} result is still

In the following, a signal-to-noise ratio E _s / N ₀ >> 1 is assumed. Then GI. (3) can be used for the actual frequency and phase offset

approach. Since the random sequence a _{v is} not known, the estimated value | a ∧ _v | used. Note that it is not the symbol that needs to be estimated but only its amount. Consequently, no frequency and phase synchronization is necessary for this. The log-likelihood function is obtained by inserting the GIn. (2,4) in GI. (1) and subsequent logarithmization

To get the same summation limits for the two thermal baths, for simplification, on the right-hand side of GI. (5), the constant independent of the estimation parameters is used

expands and thus receives the log likelihood function according to GI. ( 6 )

Illustration: The first therm in Eq. (6) describes a correlation between the frequency- and phase-compensated reception sequence with the conjugate complex sync sequence and the second therm can be seen as a measure to eliminate interference. This can be easily understood if one assumes an error-free estimate of | a ∧ _v | going out. Then the approximation

in Eq. (6) and receives with exact frequency and phase compensation

As a result, at the time of sync µ = µ With sync v -µ = a v exactly the maximum l (µ, Δω, ΔΦ) = 0 and is therefore trouble-free at the sync time.

However, the log likelihood function to be maximized in Eq. (6) is still dependent on the frequency and phase offset. The following approximations therefore aim to eliminate these dependencies. For this purpose, the log likelihood function in GI. (6) is considered for the actual frequency and phase offset. By swapping totals and real parts, you get

gemacht werden kann und damit die Log-Likelihood-Funktion unabhängig vom Phasenversatz wird. Um den Frequenzversatz analytsich schätzen zu können, werden durch eine weitere Näherung die beiden Therme in GI.(7) quadriert und erhält

At the time of sync, the inner products of the first therm are exactly real if the disturbance is neglected, so that the approximation

can be made and thus the log likelihood function is independent of the phase shift. In order to be able to estimate the frequency offset by analysis, a further approximation squares and maintains the two thermal baths in Eq. (7)

By substituting the indices you finally get

In order to shorten the spelling, the second Therm was also included in the real part bracket despite its real value. It can be seen that a correlation of the symbol energies is made in the first line with α = 0, which is not useful for MPSK. The α = 1 summand has the advantage that the estimation range of the frequency range is maximum and can also be determined analytically, as will be shown below. Therefore, only the α = 1st Summand used. The omission of the remaining summands has the consequence that a loss of signal-to-noise ratio is accepted, which is generally acceptable. This loss will be discussed again later. With this approximation, the log-likelihood function results

erhält man

Note that only S -1 summations occur. With the definitions according to GI. (8)

you get

The differential decoding of the receive sequence is shown in FIG. 6 . Note that although the sequence sync _v begins at v = 0, the differential sequences dsync _v only start at v = 1 due to the delay of one symbol period (see Eq. (9)). However, this restriction does not apply to the following algorithm if a _v is a differentially coded sequence, because then dsync _{0 is} known. This fact is illustrated again in FIG. 7 .

Maximizing the log likelihood function in Eq. (9) can thus be simplified by two cascaded maximizations: First, the maximization with respect to µ ∼ is carried out. It can be seen that the constant phase due to the frequency offset in the first therm Δ f = Δ f a reversal of corr (µ) on the real part axis causes. Hence, in good approximation, | corr (µ) | be maximized. This results in the estimation rule for the sync time µ ∧ by maximizing GI . ( 10 )

In the case of a large signal-to-noise ratio, the sole evaluation of the 1st thermal is sufficient, because then the 2.Therm gained about 3 dB is not necessary.

As mentioned at the beginning, the rule in GI. (10) also applies to the non-timing-compensated sequence. Then instead of the sequence r _v, the sequence x _{ov · v + λ must be included} λ = [0, ov -1] can be used in Eq. (8). The factor ov in the index is necessary because only samples are used at intervals of the symbol period. The index λ is necessary because the log-likelihood function must not be evaluated in the symbol grid, but in the scanning grid. The consequence of this is that the signal processing effort increases by a factor of ov .

mit korr(µ ∧) von GI.(9). Man beachte, daß der zu schätzende Frequenzversatz sowohl positiv als auch negativ sein kann. Folglich darf das Argument in GI.(11) im Sinne einer eindeutigen Bestimmung die Phase π nicht überschreiten. Damit erhält man den theoretisch zulässigen Frequenzversatz von

If you want to get the most accurate possible frequency estimate, the frequency estimate described below should not be carried out with x _v , but with r _v . The estimated frequency value results from an estimated µ ∧ from GI. (9): The log-likelihood function becomes maximum if the real part expression of GI. (9) is purely real and positive. Thus, the frequency estimate results from GI. ( 11 )

with corr (µ ∧) from GI. (9). Note that the frequency offset to be estimated can be both positive and negative. Consequently, the argument in Eq. (11) in the sense of a clear determination must not exceed phase π. This gives the theoretically permissible frequency offset of

Another derivation is obtained from the consideration that the sampling theorem for a sample / symbol period is only fulfilled for rotary pointers whose frequency is less than half the symbol frequency.
Since the permissible frequency offset in the non-data-aided process is smaller (e.g. by a factor of four in the case of MQAM), a rough frequency offset between the transmitter and receiver is permissible due to the rough estimate according to GI.

mit den Koeffizienten

Due to the approximations performed, Eq. (11) is not the optimal estimate. Alternatively, the maximum likelihood estimator for modulation methods can also be used | a v | = 1 can be implemented using a calculation rule that is only somewhat more complex. The basis for the calculation is known from the literature (Jack K. Wolf, Jay W. Schwartz: "Comparison of Estimators for Frequency Offset", IEEE Trans. On Comm., 1990, Pg. 124-127). However, in contrast to the method proposed in the literature, the phase is not averaged, but a pointer. This planar filtering has the advantage that at | Δ f / f s | → 0.5 the total pointer is more likely to be in the corresponding quadrant due to the averaging effect. With phase averaging, on the other hand, an "outlier" caused by disturbances would render the estimated value unusable. Example: Δ f / f s = -0.45 , ie the interference-free pointer should have a phase of -162 degrees. If an outlier were in the 3rd quadrant with a phase of, for example, +185 degrees, the result in phase averaging is unusable due to the sign wraps at ± 180 degrees. Consequently, the theoretically permissible frequency range of | Δ f / f s | = 0.5 be allowed. Furthermore, pointer averaging has the advantage that arithmetic-intensive argument formation is only necessary once. The calculation rule results from GI. ( 12 )

with the coefficients

The gain from the optimal estimate according to Eq. (12) increases with increasing sync length S. With S = 21, for example, the standard deviation of the estimation error is reduced by a factor of 2.

If the variance of the estimation error due to a sync sequence is too large, there is also Possibility of filtering the error variance (e.g. Kalman filter) of the individual frequency estimates to reduce. For the reasons described above, planar filtering of the Total pointer of the individual frequency estimates with subsequent standardized argument formation.

ergibt sich bei der differentiell dekodierten Folge

How large is the signal-to-noise ratio loss compared to frame synchronization with previous frequency and phase compensation using the synchronization rule according to GI. (6)? The main difference is that instead of the sequence r _v, the differentially decoded sequence dr _v is used. With

results from the differentially decoded sequence

The cross product of the noise sequence can be neglected with a large signal-to-noise ratio. It can be seen that the disturbance dn _v as well as n _{v is} uncorrelated. If you go with the modulation method MPSK | a v | = const , the standardized value results

Since the neighboring samples of the noise sequence n _{v are} uncorrelated, the noise variance in MPSK increases by a factor of 2, which corresponds to a signal-to-noise ratio loss of 3 dB. Since the performance of the frame synchronization essentially depends on the ratio of the energy of the sync sequence to the noise power density according to E _sync / N ₀ and is generally large, this loss is only a problem for transmission links with an extremely low signal-to-noise ratio and a short sync sequence.

The essential steps of frame synchronization and frequency estimation are shown again in FIG .

To demonstrate the performance, FIG. 9 shows a Monte Carlo simulation for frame synchronization of a π / 4 DQPSK transmission with a root Nyquist transmission and reception filter with a roll-off factor of r = 0.35. In this figure the eye pattern of the correlation therm is shown in Eq. (10), ie by omitting the second therm it is not even the optimal method. The extended training sequence from TETRA mobile radio with S = 15 symbols was used as the sync sequence. The frame synchronization was carried out by the non-timing compensated sequence x _v . The following parameters were also set: ov = 4, ε = 0.5 / ov = 0.125, Δ f / f s = 0.2, E s / N 0 = 8 dB, that is, the worst case is because the symbol times are exactly in the middle between the samples. Furthermore, a large frequency offset of 20% of the symbol rate and a low signal-to-noise ratio of E s / N 0 = 8 dB given. From the picture you can see that the maximum of the correlation occurs in the closest sample at the time of sync and thus the time of sync was correctly estimated. The remaining offset ε is canceled in the subsequent timing compensation.

Claims (8)

Method for determining the temporal position of a synchronization sequence in a received data stream (frame synchronization) using the principle of maximum likelihood theory, characterized in that this determination is carried out from the received data stream before the frequency and phase synchronization. Method according to Claim 1, characterized in that the maximum magnitude of the correlation between the differentially decoded received data sequence with the conjugate complex, differentially decoded synchronization sequence known at the receiving end is taken into account. Method according to claim 1, characterized in that at the same time a term for interference elimination is taken into account (equation 10). Method according to one of claims 1 to 3, characterized in that the determination is carried out before the clock synchronization. Method according to one of claims 1 to 3, characterized in that this determination is carried out only after the Tay synchronization. Method according to one of the preceding claims, characterized in that the carrier frequency deviation is then calculated from the synchronization sequence determined by its position in time according to the principle of maximum likelihood theory from the samples of the synchronization sequence. Method according to Claim 6, characterized in that in this case the maximum value of the correlation between the differentially decoded received data sequence with the conjugate complex differentially decoded synchronization sequence known at the receiving end is taken into account as an approximate solution. Method according to Claim 5 or 6, characterized in that in this case the averaging is carried out not over phase values but rather over a complex sequence with subsequent argument formation (equations 11 and 12).

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